The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  2  1  1  1  1  1  1  1  1  2  1  1  1  1  1  1  4  1  1  2  1  1  0  1  2  4  0  2  1  2  4  4  2  1
 0 12  0 12  0 12  0 12  8  4  0 12  4  0 12  8  0 12  8  4  8  0 12  4 12  4 12  4 12  0 12  0  8  0  0 12  8  0  8 12  0  8 12  8 12  0 12 12  8  0 12  8  4  4 12 12  4 12  4 12 12 12 12  0
 0  0  8  0  0  0  0  0  8  0  0  8  8  8  0  8  8  8  8  0  0  0  0  0  0  0  0  8  0  8  0  8  8  8  8  8  8  8  0  0  8  8  8  0  8  8  0  8  0  8  8  0  8  0  0  0  0  0  0  8  8  0  0  8
 0  0  0  8  0  0  0  0  0  8  0  8  0  0  8  0  8  0  8  8  8  8  0  0  0  0  0  8  0  8  8  8  8  8  0  8  0  0  8  8  8  8  0  8  8  8  0  0  0  8  0  0  8  8  8  0  8  0  0  0  0  8  8  0
 0  0  0  0  8  0  0  0  0  0  8  0  0  0  0  8  8  8  8  8  8  0  0  0  8  8  8  8  0  0  8  0  8  0  8  0  8  8  0  8  8  8  8  8  8  8  0  8  8  8  0  8  0  8  8  0  8  8  8  0  8  0  8  8
 0  0  0  0  0  8  0  0  0  0  8  8  0  8  8  8  8  0  0  8  0  0  0  8  0  8  8  8  8  8  0  0  8  8  8  0  0  0  8  0  8  0  0  0  8  8  8  8  0  0  0  8  8  0  8  0  0  0  0  8  0  0  8  0
 0  0  0  0  0  0  8  0  8  0  8  8  8  0  0  0  8  0  8  8  0  8  8  8  0  0  8  0  0  8  8  0  8  8  0  0  8  0  8  0  0  0  8  8  8  0  0  0  8  8  0  8  0  8  0  8  0  8  0  8  8  0  0  8
 0  0  0  0  0  0  0  8  0  8  8  0  0  8  8  8  0  0  8  0  8  8  8  0  8  0  8  0  8  0  8  0  8  8  0  8  8  0  0  0  0  0  0  0  8  8  8  0  8  0  8  0  8  0  8  0  8  8  0  8  8  0  0  8

generates a code of length 64 over Z16 who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+78x^56+4x^57+120x^58+28x^59+271x^60+84x^61+742x^62+140x^63+1205x^64+140x^65+726x^66+84x^67+272x^68+28x^69+66x^70+4x^71+64x^72+10x^74+19x^76+4x^80+5x^84+1x^100

The gray image is a code over GF(2) with n=512, k=12 and d=224.
This code was found by Heurico 1.16 in 0.683 seconds.